When will the Switch 2 get more 4K titles?

At what point in the Switch 2’s lifespan will we have a good amount of games that render at 4K? So far the only one I can think of is NSMBU Deluxe after the Switch 2 update. Is this something feasible for the Switch 2 at its current state over the next few years or would a mid-gen refresh be necessary for more titles to render at 4K? Everyone is expecting Nintendo to release a Lite or OLED, but what if they release a Pro instead since they are the following the PlayStation naming convention instead of coming up with something original this gen.